Two bodies at different temperature are mixed in a calorimater.Which of the following quantities remain conserved?

Options

A. Sum of the temperature of the two bodies
B. Total heat of the two bodies
C. Total internal energy of the two bodies
D. Internal energy of each body

Explanation

To solve the question of which quantities remain conserved when two bodies at different temperatures are mixed in a calorimeter, we can follow these steps:

### Step 1: Understand the System
We have two bodies, A and B, at different temperatures. Body A has a higher temperature than body B. When mixed, heat will flow from the hotter body (A) to the cooler body (B) until thermal equilibrium is reached.

**Hint:** Identify the initial conditions of the bodies involved in the calorimetry process.

### Step 2: Identify the Conservation Principles
In a closed system like a calorimeter (assuming it is perfectly insulated), we need to consider the conservation of energy. The key principle here is that energy cannot be created or destroyed, only transferred.

**Hint:** Recall the law of conservation of energy and how it applies to heat transfer.

### Step 3: Analyze the Heat Transfer
When body A loses heat, its internal energy decreases, while body B gains that heat, resulting in an increase in its internal energy. However, the total internal energy of the system (A + B) remains constant.

**Hint:** Think about how heat transfer affects the internal energy of each body.

### Step 4: Evaluate the Options
1. **Sum of the temperatures of the two bodies**: This is not conserved because temperatures change as heat is exchanged.
2. **Total heat of the body**: This is not conserved in the sense of individual heats, as heat is transferred from one body to another.
3. **Total internal energy of the two bodies**: This remains conserved as it accounts for the energy lost by one body and gained by another.
4. **Internal energy of each body**: This is not conserved individually since both bodies will change their internal energy.

**Hint:** Assess each option based on the principles of thermodynamics and the specific conditions of the calorimeter.

### Step 5: Conclusion
The only quantity that remains conserved when two bodies at different temperatures are mixed in a calorimeter is the **total internal energy of the two bodies**.

**Final Answer:** The correct option is **total internal energy of the two bodies**.